On c-lineability

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-01 DOI:10.1016/j.jmaa.2024.128916

Stanisław Kowalczyk, Małgorzata Turowska

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引用次数: 0

Abstract

In the paper we study

c

-lineability and

c

-spaceability of some families

F

of real functions defined on an interval I. The main goal is to formulate general conditions under which any non-empty family

F \subset R^{I}

of functions is

c

-spaceable or

c

-lineable. Generally, we consider the families of function of the form

F = F_{1} ∖ F_{2}

. In most cases, families of functions for which lineability and spaceability are studied have such a form. Most often, family

F_{2}

is seemingly “very close” to

F_{1}

or consists of “almost all” functions. The results obtained in this paper are a generalization of previous ideas. The main idea of our constructions is to “reproduce” one function to obtain

c

-dimensional (closed) linear space. For this “reproduction” we use the Fichtenholz-Kantorovich Theorem, applied to a countable family of pairwise disjoint intervals contained in the domain of functions from the considered class. The initial function is “squashed” and “pasted” into disjoint intervals included in the domain of constructed function.

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关于 c-lineability

本文研究定义在区间 I 上的一些实函数族 F 的可 c-线性和可 c-空间性。主要目的是提出一般条件，在这些条件下，任何非空函数族 F⊂RI 都是可 c-空间或可 c-线性的。一般来说，我们考虑 F=F1∖F2 形式的函数族。在大多数情况下，研究可线性和可空间性的函数族都具有这样的形式。大多数情况下，函数族 F2 似乎与 F1 "非常接近"，或者由 "几乎所有 "函数组成。本文所获得的结果是对以往观点的概括。我们构造的主要思想是 "再现 "一个函数，以获得 c 维（封闭）线性空间。对于这种 "再现"，我们使用费希滕霍尔茨-康托洛维奇定理，该定理适用于所考虑的函数类域中包含的成对不相交区间的可数族。初始函数被 "压扁 "并 "粘贴 "到构造函数域中的不相邻区间中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.